Finite Group Databasebeta

← #13124676

Subgroups — #13124676

Order 1664.

362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719221C211yesmaximal, characteristic
2#11719205C211yesmaximal, characteristic
3C13×#428C211yesmaximal, characteristic
4#11718781C211yesmaximal, characteristic
5#11718780C211yesmaximal, characteristic
6#11718659C211yesmaximal, characteristic
7C2×#88050C211yesmaximal, characteristic
8#11718538C212yesmaximal, complemented
9#11718536C212yesmaximal, complemented
10#11718518C212yesmaximal, complemented
11#11718515C212yesmaximal, complemented
12C22×Dic26C2211yescharacteristic
13C2×C13×M16C2211yescharacteristic
14C13×#117C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16#88180C2211yescharacteristic
17#88180C2211yescharacteristic
18#88178—22no—
19C22×#1055C2211yescharacteristic
20#88144—21no—
21#88144C2212yes—
22#88142—21no—
23#88142C2212yes—
24#88141C2212yes—
25#88141C2212yes—
26#88131—22no—
27C4×Dic26—21no—
28C4×Dic26—21no—
29C13×#107C2212yes—
30C13×#106C2212yes—
31#88056C2212yes—
32#88056C2212yes—
33#88054C2212yes—
34#88054C2212yes—
35#88050C2212yes—
36#88050C2212yes—
37#88048C2211yescharacteristic
38#88048C2211yescharacteristic
39#88047C2211yescharacteristic
40#88047C2211yescharacteristic
41C22×C4×C13—21no—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13—21no—
44C2×Dic26—21no—
45C2×Dic26—22no—
46C2×Dic26—22no—
47C2×Dic26Q814yescomplemented
48C2×Dic26C2312yes—
49C13×M16—22no—
50C2×C8×C13C2312yes—
51C13×C4⋊C4—21no—
52C13×C4⋊C4C2311yescharacteristic
53C13×C4⋊C4C2312yes—
54C13×C4⋊C4C2311yescharacteristic
55C13×C22⋊C4—21no—
56C42×C13—21no—
57C22⋊Dic13—21no—
58C22⋊Dic13D412yes—
59C4⋊Dic13—22no—
60C4⋊Dic13D411yescharacteristic
61C4⋊Dic13D411yescharacteristic
62C4⋊Dic13C2311yescharacteristic
63C4⋊Dic13C2311yescharacteristic
64#6101—22no—
65#6101—22no—
66#6101—22no—
67#6101—22no—
68C4×Dic13—21no—
69C4×Dic13—22no—
70C4×Dic13—22no—
71C4×Dic13C2312yes—
72C2×#1055—22no—
73C2×#1055C2311yescharacteristic
74C2×#1055C2311yescharacteristic
75#3082—131nomaximal, Sylow
76C23×C13C2×D411yescharacteristic
77C2×C4×C13—21no—
78C2×C4×C13—21no—
79C2×C4×C13—22no—
80C2×C4×C13—81no—
81C2×C4×C13C2×D411yescharacteristic
82C2×C4×C13C2×Q812yes—
83C2×C4×C13#4112yes—
84C2×C4×C13C2411yescharacteristic
85C2×Dic13—24no—
86C2×Dic13—22no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13C2×D412yes—
90C2×Dic13C2×D412yes—
91Dic26—24no—
92Dic26—22no—
93Dic26—82no—
94Dic26C2×Q814yes—
95C8×C13—22no—
96#1055—21no—
97#1055—21no—
98#544—131no—
99#519—131no—
100#479—132no—
101#479—132no—
102#477—132no—
103#475—132no—
104#428D1311yescharacteristic
105#427—131no—
106#424—131no—
107#419—131no—
108C2×#103—131no—
109C22×C13—21no—
110C22×C13—21no—
111C22×C13C22⋊Q812yes—
112C22×C13C22×D411yescharacteristic
113C4×C13—42no—
114C4×C13—41no—
115C4×C13—41no—
116C4×C13C22⋊Q812yes—
117C4×C13C22×Q811yescharacteristic
118C4×C13C2×#4111yescharacteristic
119Dic13—24no—
120Dic13—22no—
121Dic13—22no—
122Dic13—41no—
123Dic13—41no—
124C22×Q8—131no—
125C2×M16C2×D1311yescharacteristic
126C22×C8—131no—
127C4⋊Q8—132no—
128C4⋊Q8—261no—
129#125—132no—
130#125—261no—
131C22⋊Q8—262no—
132C4×Q8—132no—
133C4×Q8—132no—
134C4×Q8—261no—
135C4×Q8—261no—
136#117—131no—
137#117—131no—
138#117—262no—
139#117C2×D1311yescharacteristic
140C2×C4⋊C4C2×D1311yescharacteristic
141#107—131no—
142#107—131no—
143#107C2×D1312yes—
144#106—131no—
145#106—131no—
146#106C2×D1312yes—
147C4⋊C8—132no—
148C4⋊C8—132no—
149#103—132no—
150#103—132no—
151#103—132no—
152#103—132no—
153C2×C13—22no—
154C2×C13C2×C22⋊Q811yescharacteristic
155C2×C13#57711yescharacteristic
156C2×C13#57811yescharacteristic
157C2×Q8—134no—
158C2×Q8—132no—
159C2×Q8—262no—
160C2×Q8—262no—
161C2×Q8—261no—
162C22×C4—21no—
163C22×C4—261no—
164C22×C4C22×D1311yescharacteristic
165M16—22no—
166C2×C8—131no—
167C2×C8—131no—
168C2×C8—262no—
169C2×C8C22×D1312yes—
170C4⋊C4—21no—
171C4⋊C4—131no—
172C4⋊C4—131no—
173C4⋊C4—131no—
174C4⋊C4—131no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4C22×D1312yes—
181C4⋊C4C22×D1311yescharacteristic
182C4⋊C4C22×D1311yescharacteristic
183C22⋊C4—21no—
184C22⋊C4—132no—
185C22⋊C4—261no—
186C42—21no—
187C42—132no—
188C42—262no—
189C42—262no—
190C42—261no—
191C13#308211yescharacteristic, complemented, Sylow
192C23D4×D1311yescharacteristic
193Q8—134no—
194Q8—264no—
195Q8—262no—
196Q8—1042no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—81no—
201C2×C4—132no—
202C2×C4—132no—
203C2×C4—264no—
204C2×C4—262no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4#612712yes—
208C2×C4D4×D1311yescharacteristic
209C2×C4Q8×D1312yes—
210C2×C4C23×D1311yescharacteristic
211C8—22no—
212C8—261no—
213C8—261no—
214C22—21no—
215C22—21no—
216C22#8815012yes—
217C22C2×D4×D1311yescharacteristic
218C4—41no—
219C4—42no—
220C4—41no—
221C4—264no—
222C4—262no—
223C4—262no—
224C4—521no—
225C4—521no—
226C4#8815012yes—
227C4C2×#612711yescharacteristic
228C4C2×Q8×D1311yescharacteristic
229C2—22no—
230C2C2×#8815011yescharacteristic
231C2#1171948011yescharacteristic
232C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#428C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#428D13
hypocenterC13#3082
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
8. #11718538C2semidirect
9. #11718536C2semidirect
10. #11718518C2semidirect
11. #11718515C2semidirect
47. C2×Dic26Q8semidirect
191. C13#3082semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117192212
#117192052
C13×#4282
#117187812
#117187802
#117186592
C2×#880502
#117185382
#117185362
#117185182
#117185152
#308213